Difference between revisions of "2011 AMC 10B Problems/Problem 24"
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==Solution== | ==Solution== | ||
− | We see that for the graph of <math>y=mx+2</math> to not pass through any lattice points its denominator must be greater | + | We see that for the graph of <math>y=mx+2</math> to not pass through any lattice points its denominator must be greater than <math>100</math>. We see that the nearest fraction bigger than <math>\frac{1}{2}</math> that does not have its denominator over <math>100</math> is <math>\boxed{50/99}</math>. |
==See Also== | ==See Also== | ||
{{AMC10 box|year=2011|ab=B|num-a=25|num-b=23}} | {{AMC10 box|year=2011|ab=B|num-a=25|num-b=23}} | ||
{{MAA Notice}} | {{MAA Notice}} |
Revision as of 11:27, 22 July 2013
Problem
A lattice point in an -coordinate system is any point where both and are integers. The graph of passes through no lattice point with for all such that . What is the maximum possible value of ?
Solution
We see that for the graph of to not pass through any lattice points its denominator must be greater than . We see that the nearest fraction bigger than that does not have its denominator over is .
See Also
2011 AMC 10B (Problems • Answer Key • Resources) | ||
Preceded by Problem 23 |
Followed by Problem 25 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 | ||
All AMC 10 Problems and Solutions |
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